On the convergence of implicit iteration process with error for a finite family of asymptotically nonexpansive mappings |
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Authors: | SS Chang KK Tan |
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Institution: | a Department of Mathematics, Yibin University, Yibin, Sichuan 644007, China b Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, China c Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia, Canada B3H 3J5 d Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong |
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Abstract: | The purpose of this paper is to study the weak and strong convergence of implicit iteration process with errors to a common fixed point for a finite family of asymptotically nonexpansive mappings and nonexpansive mappings in Banach spaces. The results presented in this paper extend and improve the corresponding results of H. Bauschke, The approximation of fixed points of compositions of nonexpansive mappings in Hilbert space, J. Math. Anal. Appl. 202 (1996) 150-159; B. Halpern, Fixed points of nonexpansive maps, Bull. Amer. Math. Soc. 73 (1967) 957-961; P.L. Lions, Approximation de points fixes de contractions, C. R. Acad. Sci. Paris, Ser. A 284 (1977), 1357-1359; S. Reich, Strong convergence theorems for resolvents of accretive operators in Banach spaces, J. Math. Anal. Appl. 75 (1980) 287-292; Z.H. Sun, Strong convergence of an implicit iteration process for a finite family of asymptotically quasi-nonexpansive mappings, J. Math. Anal. Appl. 286 (2003) 351-358; R. Wittmann, Approximation of fixed points of nonexpansive mappings, Arch. Math. 58 (1992) 486-491; H.K. Xu, M.G. Ori, An implicit iterative process for nonexpansive mappings, Numer. Funct. Anal. Optimiz. 22 (2001) 767-773; Y.Y. Zhou, S.S. Chang, Convergence of implicit iterative process for a finite family of asymptotically nonexpansive mappings in Banach spaces, Numer. Funct. Anal. Optimiz. 23 (2002) 911-921]. |
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Keywords: | Asymptotically nonexpansive mapping Nonexpansive mapping Implicit iterative sequence with errors for a finite family Common fixed point Opial condition Demi-closed principle Semi-compactness |
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